Least Common Multiple (LCM) of 199 and 71
The least common multiple (LCM) of 199 and 71 is 14129.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 199 and 71?
First, calculate the GCD of 199 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 71 = 2 remainder 57 |
| 2 | 71 ÷ 57 = 1 remainder 14 |
| 3 | 57 ÷ 14 = 4 remainder 1 |
| 4 | 14 ÷ 1 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 24 and 139 | 3336 |
| 67 and 107 | 7169 |
| 78 and 53 | 4134 |
| 101 and 109 | 11009 |
| 96 and 128 | 384 |